47. The Harmonic or Byzantine or Romani or Hungarian or Ukrainian or Flamenco or Mohammedan minor and double minor scale, (also mode of Arabic Niavent scale)

The Byzantine double minor (or harmonic double minor scale )  scale is 1-3-1-2-1-3-1 in semitones, In other words it is the know oriental folk tetra-chord
1-3-1 doubled and linked in the middle with its repetition with a whole tone. It is also a mode of the Arabic-like scale Niavent in the Greek folk music (Niavent=2-1-3-1-1-3-1 )

Some times as Byzantine scale is mentioned the 7 notes scale, which is also called Harmonic double minor


 1-3 - 1 - 2 - 1 - 3 - 1 

Of course the Byzantine scales were many and were 7-notes but with frequencies not possible to play in our western 12-notes Bach scale.

The chords that fit to  the Byzantine or Romani or Hungarian double minor scale ,( we take here as an example the D Romani or Hungarian double  minor) are the next:

Notes of this scale:

D; E; F; G#/Ab; A; A#/Bb; C#/Db; D;

Interval structure of this scale:

2-1-3-1-1-3-1

Chords that fit in this scale:

Normal Triads: C#     C#m     C#aug     Dm     Ddim     Faug     A     Aaug     A#     A#m     A#dim  Other Triads: Dsus2     Asus4  4 Notes Chords: C#6     C#m6     Dm(maj7)     E7b5     Amaj7     A#maj7     A#7     A#7b5     A#m7     A#m(maj7)     A#m7b5

Two nice positions of the  Romani (Gypsy)  double minor scale are the next. The first is the shape of major7 chord together with its shift by one semitone! The rule of this shape is 2 notes per string.

Other positions are the next 

The Byzantine or Romani (Gyspy)  or Mohammedan non-double  minor  scale is essentially (a cyclic permutation of )  the harmonic minor scale

1) Harmonic minor (called also mode of Hijazz ) = (1-3-1)-2-(-1-2-2),


A mode (cyclic permutation) of the harmonic minor is called  also 7-tone Blue-scale in American folk music.

Chords of the harmonic minor (intervals 2-1-2-2-1-3-1):



Triads:           min              dim aug         min           maj         maj       dim
Extended
4-notes chord: min/maj7    m7b5 maj7#5 min7 dom7 maj7     dim7

For example for the A harmonic minor(A,B,C,D,E,F,G#) (intervals 2-1-2-2-1-3-1) the chords are

i	iidim	III	iv	V	VI	VII
Amin	Bdim	Caug	Dmin	Emaj	Fmaj	G#dim
Aminmaj7	Bm7b5	Cmaj7#5	Dmin7	E7	Fmaj7	G#dim7

Typical progression

Typical chord progressions in A harmonic minor
i - iv - V7	Am - Dm - E7
ii - V7 - i	Bm7b5 - E7 - Am

More general the chords that fit to the harmonic minor (not taking necessarily the notes in alternating order , that is take one leave one  or 1-3-5  etc) are the next

Notes of this scale:

A; B; C; D; E; F; G#/Ab; A;

Interval structure of this scale:

2-1-2-2-1-3-1

Chords that fit in this scale:

Normal Triads: Caug     Dm     Ddim     E     Eaug     F     Fm     Fdim     G#aug     G#dim     Am     Bdim  Other Triads: Dsus2     Esus4     Asus4     Asus2  4 Notes Chords: Dm6     Dm7     Dm7b5     Dº7     D7sus2     E7     E7#5     E7sus4     F6     Fm6     Fmaj7     Fm(maj7)     Fº7     G#º7     Am(maj7)     Bm7b5     Bº7

Again a nice way to play the Harmonic minor on the fretboard with the rule of this shape is 2 notes per string, is the next

5 other ways to play this scale on the guitar fretboard are the next 

Two variations of the Byzantine double minor scale are the Persian and inverse Persian scales or

Persian scale or todi theta scale=(1-3-1-1-2-3-1) 
E.g. starting from C

Notes of this scale:

C; C#/Db; E; F; F#/Gb; G#/Ab; B; C;

Interval structure of this scale:

h (W+h) h h W (W+h) h

Chords that fit in this scale:

Normal Triads: C#     C#m     Caug     E     Eaug     Fm     Fdim     G#aug  Other Triads: C#sus4     Esus2     F#sus4     F#sus2     Bsus4     Bsus2  4 Notes Chords: C#maj7     C#7     C#m7     C#m(maj7)     C#7sus4     E6     Fm(maj7)     F#7sus4     F#7sus2     G#7#5

Inverse Persian scale or Purvi Theta scale= (3-1-1-3-2-1-1) 

E.g. starting from C

Notes of this scale:

C; C#/Db; E; F#/Gb; G; G#/Ab; B; C;

Interval structure of this scale:

h (W+h) W h h (W+h) h

Chords that fit in this scale:

Normal Triads: C     C#m     Caug     C#dim     E     Em     Eaug     G#aug  Other Triads: C#sus4     Esus2     F#sus4     F#sus2     Bsus4     Bsus2  4 Notes Chords: Cmaj7     C#m7     C#m(maj7)     C#m7b5     C#7sus4     E6     Em6     F#7sus4     F#7sus2     G#7#5     C\E     C\G

And a simple video comparing the chords in natural and harmonic minor

https://www.youtube.com/watch?v=FlRPPyKYKrQ

46. The 7, maj7, 6, m6, dim, and aug versions of the open chords.

(This post has not been written completely yet)

In this post we list the shapes of the maj7, 6, m6, dim, and aug versions of the open chords.

45. Relations of classical diatonic scales defined by common notes ,chords, triads and tetra-chords.

44. Placing the harmonic structure of 24-cycle of chords by 4ths and relatives, on the fretboard by the DAE system.

Here we will show how the relative chords appear by the DAE system on the guitar fretboard. Inother words how by looking at the fretboard we may find the harmonic structure of relaltive chords of a chord, directly on the fretboard. Also how the resolution of chords by intervals of 4ths (dominant7th-root) also appear in the guitar fretboard, using the DAE system. Again this is very susefull as we "see" the structure of harmony directly on the chord patterns on the fretboard. As the 24 cycle of chords (see post 32) is also a rule of modulations, we will have how such a rule of modulations appears on the guitar fretboard. Tonality then will be simple an arc of 6-chord on this 24 cycle. As the above method is beyond tonality , the concept of tonality and modulation will not block  us much when we play the chord progressions and think the harmony we are playing.

The most direct representation of the 24-cycle of all chords is on the fretboard of  6-string bass or 6-string guitar which is tuned at all strings by pure 4ths.
Then this pattern of the chords appears naturally on the fretboard of a bass or guitar tuned on all chords by pure 4ths!  In the next image we see only the positions or arpeggio of the Cmaj chord, and we can easily add the lower relative Am.Then put the same for all other positions of the other chords. The vertical direction from lower to higher notes is the same as the direction of the 24-cycle of chords. Every vertical path inside a fret, spans with 3 of the positions of the major chords a diatonic scale.

THE USUAL 4 WAYS TO WALK INSIDE THE FRETBOARD ARE

1) By knowing patterns of scales

2) By known the shapes of chords, and then walk around the chord shapes

3) By knowing all the names of the notes of all the frets of the fretboard

4) Without any mental image, but simply by the feeling of the desired note, and the feeling-familiarization of the fretboard.

E.g. see https://www.youtube.com/watch?v=d7-ZnzAqt0A

The 5 -triads in successive resolution harmonic relation on the fretboard.

The best way to learn the fretboard is without mental images but only the feeling of the notes at each fret.But this takes too much practice and familiarization with the fretboard.

On the other hand the best way to learn all the fretboard through mental images,rather than feeling,is not by patterns of scales, neither by the names of all the notes of the frets, but rather with sufficient many chord-shapes that almost cover all the fretboard. And even better  if these chords are organized in to easy repeating patterns. Here we describe a method, based on the triads of chords in shapes of E, A, D, so that each is relative to its previous, at the harmonic relation of successive resolution in the cycle of 4ths (see also post 30, 23).

Here we list the chords of shapes E, A, D,on the notes of the e4-string

e4, g4, a4, b4, d5, 

For the symbolism of chords placed on the fretboard, see post 23

chords (E- shape)	chords (A- shape)	chords (D- shape)
e4  (0E)E	(0A)A	(0D)D
g4 (3E)A	(3A)C	(3D)F
a4 (5E)A	(5A)D	(5D)G
b4 (7E)B	(7A)E	(7D)A
d5 (10E)D	(10A)G	(10D)C

When adding the minor chords of the diatonic scale, if the roots is an A-shape we have the following positions

With A-shape as root,  where the I, and V are on the same fret. In the symbolism of post 23 the  (nA)X means at n-th fret play the shape A and it sounds as chord X. Here instead of X we will utilize the Latin symbols of the steps in a major scale, as it is standard in Jazz with small if the chord is minor and capital if the chord is major

So the chords I, ii, iii, IV, V, vi, vii, are played on the fretboard only as shapes A and E as follows

I=(nA)I, ii=((n+2)Am)ii , iii= ((n-1)D)iii,  (nD)IV,  V=(nE)V,  vi=((n+2)Em)vi  

vii=((n-1)dim7)vii.

In short the three main major chords I, IV, V are the 

I=(nA)I, IV=((n)D)IV, V=(nE)V. 

As for the equivalence of chords in different positions and shapes on the fretboard for the  shapes D, A and E hold the rules

1)The D shape sounds as the same chord with A shape 5 frets higher , In symbols e.g. (1D)D=(5A)D and in general (nD)X=((n+5)A)X

2) The A shape sounds as the same chord with E shape 5 frets higher , In symbols e.g. (1A)A=(5E)A and in general (nA)X=((n+5)E)X

3) The E shape sounds as the same chord with D shape 2 frets higher , In symbols e.g. (1E)E=(2D)E and in general (nE)X=((n+2)D)X

In relation with the 24-chords cycle of chords by intervals of 4ths  the DAE system has the next keys and correspondences (with the symbolism of chords on the fretboard as in post 23 ).

 The sequence  X=(nE)Y1, X+1=((n)A)Y2, X+2=((n)D)Y3 is of course a vertical sequenceof chords in thefretbaird and a sequence of 3 successive chords in the cycle of 4ths and symbols of post 34. Now after the X+2=((n)D)Y3, the cycle of 4ths continues either lower in the fretboard or higher in the fretboard

1) Lower in the fretboard is X+3=((n-2)A)Y4

2) Higher in the fretboard is X+3=((n+3)E)Y4

From this point of view, the area of the open chords of the guitar, is simply two such vertical 3-sequences of chords on the cycle of 4ths, as the C-shape is essentially a ((n-3)D)Y chord and D-shape and the G-shape is a ((n-2)A)Y chord and A-shape.